Question Number 153583 by pete last updated on 08/Sep/21 $$\mathrm{If}\:{fog}\left({x}\right)=\frac{\mathrm{2}{x}−\mathrm{1}}{{x}}\:\mathrm{and}\:\mathrm{g}\left({x}\right)=\mathrm{5}{x}+\mathrm{2},\:\mathrm{find} \\ $$$${f}\left({x}\right). \\ $$ Commented by otchereabdullai@gmail.com last updated on 08/Sep/21 $$\mathrm{nice}\:\mathrm{question} \\ $$ Commented…
Question Number 88040 by peter frank last updated on 08/Apr/20 $${Find}\:{the}\:{max}\:{and}\:{min} \\ $$$${of}\:{function} \\ $$$$\frac{{a}+{b}\mathrm{sin}\:{x}}{{b}+{a}\mathrm{sin}\:{x}} \\ $$$${where}\:{b}>{a}>\mathrm{0}\:{in}\:{the}\: \\ $$$${interval}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}\pi.{sketch} \\ $$$${a}=\mathrm{4}\:{and}\:{b}=\mathrm{5} \\ $$ Commented by…
Question Number 88039 by peter frank last updated on 08/Apr/20 $${Obtain}\:{the}\:{first}\:{four} \\ $$$${term}\:{of}\:{the}\:{expansion} \\ $$$$\left(\mathrm{4}−{x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} {when} \\ $$$$\left(\mathrm{1}\right)\mid{x}\mid<\mathrm{1} \\ $$$$\left({ii}\right)\mid{x}\mid>\mathrm{1} \\ $$ Answered by Rio…
Question Number 22503 by Tinkutara last updated on 19/Oct/17 $$\mathrm{If}\:\left({a}\:+\:{bx}\right)^{−\mathrm{2}} \:=\:\frac{\mathrm{1}}{\mathrm{4}}\:−\:\mathrm{3}{x}\:+\:…,\:\mathrm{then}\:\left({a},\:{b}\right)\:= \\ $$ Commented by mrW1 last updated on 19/Oct/17 $$\left(\mathrm{a}+\mathrm{bx}\right)^{−\mathrm{2}} =\mathrm{a}^{−\mathrm{2}} \left(\mathrm{1}+\frac{\mathrm{bx}}{\mathrm{a}}\right)^{−\mathrm{2}} =\mathrm{a}^{−\mathrm{2}} \left[\mathrm{1}−\mathrm{2}×\frac{\mathrm{bx}}{\mathrm{a}}+…\right]…
Question Number 153571 by mathdanisur last updated on 08/Sep/21 $$\mathrm{Find}\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}n}\centerdot\left(\frac{\pi^{\mathrm{2}} }{\mathrm{4}}\:-\:\mathrm{a}_{\boldsymbol{\mathrm{n}}} ^{\mathrm{2}} \right)\:=\:? \\ $$$$\mathrm{where}\:\:\mathrm{a}_{\boldsymbol{\mathrm{n}}} =\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\mathrm{arctan}\left(\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} -\mathrm{k}+\mathrm{1}}\right) \\ $$ Answered by mnjuly1970…
Question Number 22491 by Tinkutara last updated on 19/Oct/17 $$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{r}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{1}\:−\:\mathrm{2}{x}\right)^{−\mathrm{1}/\mathrm{2}} \:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\frac{\left(\mathrm{2}{r}\right)!}{\left({r}!\right)^{\mathrm{2}} } \\ $$$$\left(\mathrm{2}\right)\:\frac{\left(\mathrm{2}{r}\right)!}{\mathrm{2}^{{r}} \:\left({r}!\right)^{\mathrm{2}} } \\ $$$$\left(\mathrm{3}\right)\:\frac{\left(\mathrm{2}{r}\right)!}{\left({r}!\right)^{\mathrm{2}} \:\mathrm{2}^{\mathrm{2}{r}} }…
Question Number 88014 by ajfour last updated on 07/Apr/20 $${If}\:{there}\:{is}\:{no}\:{second}'{s}\:{hand}\:{on} \\ $$$${a}\:{clock}\:{and}\:{the}\:{minute}\:{and}\:{hour} \\ $$$${hand}\:{move}\:{in}\:{continuous}\:{fashion}, \\ $$$${then}\:{exactly}\:{at}\:{what}\:{time}\:{between} \\ $$$$\mathrm{02}:\mathrm{10}\:\:{and}\:\mathrm{02}:\mathrm{15}\:{does}\:{the}\:{position} \\ $$$${of}\:{the}\:{two}\:{hands}\:{exactly}\:{coincide}? \\ $$ Answered by mr…
Question Number 22474 by Tinkutara last updated on 19/Oct/17 $$\mathrm{Let}\:{R}\:=\:\left(\mathrm{5}\sqrt{\mathrm{5}}\:+\:\mathrm{11}\right)^{\mathrm{2}{n}+\mathrm{1}} \:\mathrm{and}\:{f}\:=\:{R}\:−\:\left[{R}\right], \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:{Rf}\:=\:\mathrm{4}^{\mathrm{2}{n}+\mathrm{1}} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 22472 by Tinkutara last updated on 18/Oct/17 $$\mathrm{If}\:{x}^{{x}} \centerdot{y}^{{y}} \centerdot{z}^{{z}} \:=\:{x}^{{y}} \centerdot{y}^{{z}} \centerdot{z}^{{x}} \:=\:{x}^{{z}} \centerdot{y}^{{x}} \centerdot{z}^{{y}} \:\mathrm{such} \\ $$$$\mathrm{that}\:{x},\:{y}\:\mathrm{and}\:{z}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{greater}\:\mathrm{than}\:\mathrm{1},\:\mathrm{then}\:\mathrm{which}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{true}\:\mathrm{for}\:\mathrm{any}\:\mathrm{of}\:\mathrm{the}…
Question Number 22468 by Tinkutara last updated on 18/Oct/17 $$\mathrm{If}\:{a}_{{r}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{r}} \:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\left(\mathrm{1}\:+\:{x}\:+\:{x}^{\mathrm{2}} \right)^{{n}} ,\:\mathrm{then} \\ $$$${a}_{\mathrm{1}} \:−\:\mathrm{2}{a}_{\mathrm{2}} \:+\:\mathrm{3}{a}_{\mathrm{3}} \:−\:…….\:\mathrm{2}{na}_{\mathrm{2}{n}} \:= \\ $$ Terms…